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In the upper branch of the game tree, "offer" is chosen by the system, and the user can respond with "accept" or "reject". For the dialogue [offer,accept], it becomes mutual that bel(have-seat), and that intend(book-flight-window), since these are preconditions. Therefore both of these should increase in the updated decaying-average model, possibly crossing the decision surface so that the system will not take the initiative the next time around. For [offer,reject] bel(have-seat) should increase, whereas intend(window-seat) should decrease. The dry-land algorithm is redundant in this case, since both bel(have-seat) and intend(window-seat) are updated by precondition inference.
An example point was taken, [bel(have-seat),intend(window-seat)] = [0.5,0.9], and the belief model changed to :
bel(have-seat) = 1 was mutual and intend(window-seat) = 1 was mutual for [offer,accept]
bel(have-seat) = 1 was mutual for and intend(any-seat) = 1 was mutual for [offer,reject].